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The index of an Eisenstein ideal and multiplicity one. (English) Zbl 1338.11057

Let \(X_0(N)\) be the modular curve of level \(\Gamma_0(N)\) and let \(J_0(N)\) be the Jacobian of \(X_0(N)\). There is an action of the Hecke algebra \(\mathbb{T}(N)\) on \(J_0(N)\). Let \(\mathfrak{m}\) be an Eisenstein maximal ideal of \(\mathbb{T}(N)\). In this article, the author generalizes the well-known result of B. Mazur [Publ. Math., Inst. Hautes Étud. Sci. 47, 33–186 (1977; Zbl 0394.14008)] on \(\mathfrak{m}\)-torsion of \(J_0(N)\) to the square-free level.

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
11F80 Galois representations

Citations:

Zbl 0394.14008

Software:

SageMath
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References:

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